Fault-tolerant path embedding in folded hypercubes with both node and edge faults

The folded hypercube FQn is a well-known variation of the hypercube structure. FQn is superior to Qn in many measurements, such as diameter, fault diameter, connectivity, and so on. Let (resp. ) denote the set of faulty nodes (resp. faulty edges) in FQn. In the case that all nodes in FQn are fault-free, it has been shown that FQn contains a fault-free path of length 2n−1 (resp. 2n−2) between any two nodes of odd (resp. even) distance if , where n≥1 is odd; and FQn contains a fault-free path of length 2n−1 between any two nodes if , where n≥2 is even. In this paper, we extend the above result to obtain two further properties, which consider both node and edge faults, as follows: 1.FQn contains a fault-free path of length at least (resp. ) between any two fault-free nodes of odd (resp. even) distance if , where n≥1 is odd.2.FQn contains a fault-free path of length at least between any two fault-free nodes if , where n≥2 is even.